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Q61 (CISF/2022) Miscellaneous & General Knowledge › Important Days, Places & Events

From a pack of 5 green balls and 4 red balls, 2 balls are drawn at random. What is the probability that both the balls are of the same colour ?

Explanation

To find the probability that both balls are of the same colour, we must calculate the total number of ways to draw 2 balls and the number of ways to draw either 2 green balls or 2 red balls.

  1. Total Outcomes: The number of ways to select 2 balls from a total of 9 (5 green + 4 red) is 9C2 = (9 × 8) / (2 × 1) = 36.
  2. Favourable Outcomes (Green): The number of ways to select 2 green balls from 5 is 5C2 = (5 × 4) / (2 × 1) = 10.
  3. Favourable Outcomes (Red): The number of ways to select 2 red balls from 4 is 4C2 = (4 × 3) / (2 × 1) = 6.

Total favourable outcomes = 10 + 6 = 16.
Probability = Favourable Outcomes / Total Outcomes = 16/36 = 4/9.

Therefore, the probability that both balls are of the same colour is 4/9.

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